Question

The Boston Transit Authority wants to determine whether there is any need for changes in the frequency of service over certain bus routes. The transit authority needs to know whether the frequency of service should increase, decrease, or remain the same.
The transit authority determined that if the average number of miles traveled by bus over the routes in question by all residents of a given area is about 5 per day, then no change will be necessary. If the average number of miles traveled per person per day is either more than 5 or less than 5, then changes in service may be necessary. The authority wants, therefore, to test the null hypothesis that the average number of miles traveled per person per day is 5.0 versus the alternative hypothesis that the average is not 5.0 miles. The required level of significance for this test is α = 0.05. A random sample of 120 residents of the area is taken, and the sample mean is found to be 2.3 miles per resident per day and the sample standard deviation 1.5 miles. Advise the authority on what should be done. Explain your recommendation. Could you state the same result at different levels of significance? Explain.